Archive for April, 2011

181(1): Relativistic Hamilton Jacobi Equation for R

Friday, April 29th, 2011

Feed: Dr. Myron Evans
Posted on: Thursday, April 28, 2011 7:17 AM
Author: metric345
Subject: 181(1): Relativistic Hamilton Jacobi Equation for R

This note introduces this approach to particle collisions, one in which the hamiltonian is constant and defined in the usual way by Eq. (2), but one which implements the following equation for the covariant mass:

m = m sub 0 + m sub 1

where m is the covariant mass and m sub 0 the measured mass. As in UFT 158 ff., the covariant mass is no longer constant, but m sub 0 is constant. I recommend studying these background notes, they are seminars or lectures in preparation for each new paper, and the feedback shows that they have been cited 300,000 times in only three years. Obviously, the readers find them useful. The suggestion to post these notes was made two or three years ago by David Feustel, sometime of Cornell University. They are picked up by search engines and referring URL’s. After all, a citation is in the last analysis a reference to other work. It makes no difference whether this is a reference from a published paper or from an electronic URL (unique reference locator).


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180(2): New ECE Wave Equation

Friday, April 22nd, 2011

Feed: Dr. Myron Evans
Posted on: Friday, April 22, 2011 7:47 AM
Author: metric345
Subject: 180(2): New ECE Wave Equation

This is Eq. (1), in which omega and kappa are properties of spacetime. Eq. (2) is the new ECE wave equation of electromagnetism, and eq. (5) collects the expressions for R. The covariant mass and metrical methods are compared in eqs. (3) and (4). Eq. (2) is a new expression for the generally covariant Proca equation of the boson with mass. It is seen that spacetime is in general dispersive, because in general:

omega / c is not equal to kappa.

In other words spacetime is a dielectric with loss and permittivity, explaining the origin of the cosmological shift without Big Bang (UFT 49 and 118). For a massless particle:

omega / c = kappa

and the generally covariant d’Alembert equation is the result. In the received opinion of relativity, due to Einstein and others, it can be seen from eq. (5) that the mass m sub 0 is always the same, so R is always that of the free particle:

R = (m sub 0 c / h bar) squared.

However, keeping m sub 0 constant results in disaster for particle physics, as shown in UFT 158 ff and UFT 171. One can now challenge with confidence the very idea of elementary particles, and in fact it is well known that in relativity, there are no particles, there is only geometry and a scaling factor called “mass”, m sub 0. In covariant mass theory the scaling factor is dispensed with, so mass itself becomes part of geometry. Everything in physics becomes geometry, as required by the philosophy of relativity.


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Remarks about UFT 179

Friday, April 22nd, 2011

Feed: Dr. Myron Evans
Posted on: Thursday, April 21, 2011 10:49 AM
Author: metric345
Subject: Remarks about UFT 179

The mass is defined for a given E and p, at some future stage computer algebra can be applied to experiment with the results. The expression for the mass is

m = (E squared – p squared c squared) power half / c squared

where E and p are constants of motion. The received opinion would use a constant m sub 0, but the covariant mass m is allowed to be a function of E and p, and so is allowed to vary as indicated by UFT 158 ff and UFT 171. For different dynamical situations E and p are different constants of motion.

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The Scalar R

Thursday, April 21st, 2011

Feed: Dr. Myron Evans
Posted on: Wednesday, April 20, 2011 11:21 AM
Author: metric345
Subject: The Scalar R

Many thanks in turn! I am about ready to write up UFT 179 on the new discovery that the energy equation of general relativity has the same format as the Einstein energy equation of special relativity, provided the measured mass m0 is replaced by the covariant mass. The latter can be found from metrical methods. So the fermion and Schroedinger equations have the same format in general relativity, the mass m0 being replaced by the covariant mass m. This method predicts a large number of new spectral effects. The covariant mass of UFT 158 ff. can also be obtained from metrical methods. The covariant mass m is related to R by:

R = (mc / h bar) squared

so R can also be found from metrical methods.

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Implementation of the Code Package WIEN for Force Eigenvalues

Sunday, April 10th, 2011

Feed: Dr. Myron Evans
Posted on: Wednesday, April 06, 2011 7:03 AM
Author: metric345
Subject: Implementation of the Code Package WIEN for Force Eigenvalues

It could be that more up to date versions of code address this problem more and more accurately as computers become faster and more powerful. Probably there are iterative procedures for finding the right spectrum after first omitting kappa. The 2 x 2 matrix method looks very interesting. Novak’s starting equations (15) and (16) certainly give the complete H spectrum as shown in Merzbacher and numerous other textbooks. The method given by Atkins also gives the complete H spectrum. The Novak method omits the last term on the LHS of his eq. (17), but retains the l (l + 1) term. However, in his eq. (19) he uses kappa (kappa + 1) = l(l + 1), and this is not self consistent because l(l +1) is first assumed to be zero, then in eq. (21), non-zero. It should be possible to solve eq. (17) of Novak with computer algebra to get g with no approximations, and then get the forces using

(H hat – epsilon) del g = F g

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Corrigenda Note 178(5)

Thursday, April 7th, 2011

Feed: Dr. Myron Evans
Posted on: Wednesday, April 06, 2011 7:16 AM
Author: metric345
Subject: Corrigenda Note 178(5)

Thanks to Dr Horst Eckardt for two corrigenda:

1) In Eq. (19), replace minus by plus before (epsilon – V) / (2 m c squared).
2) In Eq. (30) the first term is plus and second term minus.

These slips do not affect the final result (41). The mass term is given by some authors and not by others (e.g. Ryder does not give it, and he omits the spin orbit and Darwin terms). It comes from the non-relativistic approximation of kinetic energy given in eq. (22), i.e. epsilon about p squared / (2m). This approximate epsilon is then put back in the third RHS term of eq. (21) to give:

sigma dot p p squared sigma dot p phi / (8 m cubed c squared) = p fourth / (8 m cubed c squared)

with p = – i h bar del.

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